This has not been my experience at all! My first broody hen was a Black Sexlink I had purchased from the feed store as a day-old chick. She was 17 months when she went broody in August but she sat faithfully (in a record hot summer) on those eggs until 7 of the 12 she started with, hatched. She was an excellent mother, and didn't lose a single chick. She kept them with her until they were 15 weeks old!
Since then I've had an uncountable number of broody hens. I've only had one that wasn't very good at it - and she was one of the chicks raised by that very first broody hen. She had a mother until she was 15 weeks old, so when she went broody this summer, I thought "awesome". She hatched 3 chicks, and immediately rejected and pecked one of them, kicking it out of the nest. If it hadn't been summer, it would have died. As it was, I found it cowering in terror in a corner. I retrieved it and gave it to another broody hen, who, fortunately, accepted and raised it. Meanwhile, the first hen still had two of her chicks. She was in a segregated small pen I use just for broodies, and she did fine in there, but then I let her out with the flock and she promptly lost one of her chicks. It may not have been her fault - I did have a hawk visit that day - but nevertheless, she failed to keep her chick safe. So, with one remaining chick, she continued on, but at night, abandoned the chick to go and roost in the coop. I wound up putting her remaining chick in with another broody who adopted it, even though it was a couple weeks older than her chicks. During the night she would tuck them all under her to sleep, but during the day the first hen would join her and the two of them would stay with the chicks, helping them learn to forage. During all of this though, at night she left them and went to roost by herself.
Every other broody hen I've had has done an excellent job - and I think with the exception of the "bad" mom, who was herself broody raised, every broody I've had, hatched in an incubator.